Research Papers in Economics

No. 5/10

Drobisch´s Legacy to Price Statistics

Ludwig von Auer

Drobisch’s Legacy to Price Statisticsby

Ludwig von Auer∗

Universität Trier, Germany

April 2010

Short Summary of Paper

In order to provide information concerning the significant contributions to priceindex theory made by Moritz Wilhelm Drobisch (1802-1896), this paper presentsan account of his pioneering scientific achievements together with a synopsis of hispersonal and professional life. He was the first to formulate the unit value index aswell as the Laspeyres and Paasche price indices. These three indices are the key forthe official inflation measurements that are made around the world today.

Keywords: Price, Inflation, Index Theory, MeasurementJEL Classification: C43, E31, E52

∗I was motivated to write this article by the retirement of a highly esteemed colleague, Petervon der Lippe at the Universität Duisburg-Essen. His enthusiasm for price statistics and theiroriginators was infectious. This paper is testimony to that fact. I am indebted to Nick Barton andClaudia Haller for excellent research assistance. John Brennan’s generous advice greatly improvedthe readability of this paper. Two anonymous referees and the editors of this journal providedseveral invaluable comments.

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Long Summary of Paper

This paper attempts to establish a greater awareness among researchers for thenoteworthy contributions to price index theory made by Moritz Wilhelm Drobisch(1802-1896), a German mathematician and philosopher at the Universität Leipzig.Few economists and statisticians are aware of the fact that neither Étienne Laspeyresnor Hermann Paasche originally devised the well-known price indices that presentlycarry their names. Moritz Wilhelm Drobisch was the first to publish them in 1871 ina treatise and, shortly thereafter, in an abridged version that appeared in this veryjournal. He rejected them, however, because in his view they were inappropriatemeasures of inflation. Instead, he devised the unit value index, which he regardedas superior to all other price index formulas. This paper contains a descriptionof his pioneering scientific achievements together with a synopsis of his personaland professional life. Its purpose is to give credit where credit is due, but moreimportantly, it attempts to recognize these seminal contributions in light of thefactors that have tarnished them in the recorded annals of price index history. Itattempts to put them into their proper perspective.

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1 Introduction

If asked to name the two price index formulas that are the most renowned, eco-nomists and statisticians alike would probably answer in unison, the Laspeyres andPaasche indices. The references most often quoted are their famous articles pub-lished in 1871 and 1874 in this very journal. Unfortunately, few researchers areaware, however, that neither of these two scholars, Étienne Laspeyres (1834-1913)nor Hermann Paasche (1851-1925), devised these two index formulas.2 Instead, theyfirst appeared in a publication authored by Moritz Wilhelm Drobisch (1802-1896),a mathematician and philosopher at the Universität Leipzig. In addition, he alsodeveloped the unit value index. These three price indices are the key to the officialinflation measurements made around the world today. Therefore, this distinguishedscholar’s contribution to price statistical research should be appropriately acclaimedand acknowledged.

Figure 1: Three German Price Statisticians.

In 1871, the Königliche Sächsische Gesellschaft der Wissenschaften (Royal Sci-entific Society of Saxony) published a treatise written by its founder Drobisch(1871a). Later that year, Drobisch (1871b) wrote an abridged version of that treat-ise, which appeared in this journal. Today it is known that these two publicationsprovide the scientific basis for modern applied price statistics. In the original pa-per, Drobisch (1871a: 37-39) proposed three index formulas: the unit value indexand a pair of index formulas that subsequently became known as the Laspeyres andPaasche indices. Among these three formulas, he clearly expressed a preference forthe unit value index, which he thought was an optimal price index formula.

2Notable exceptions are Balk (2008: 7 and 8, footnotes 11 and 13) and ILO et al. (2004: 265,footnotes 7 and 8).

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At that time, many prominent economists and statisticians considered thesearticles. Not surprisingly, Étienne Laspeyres and Hermann Paasche were drawn tothem as well. In his response to Drobisch’s (1871a) publication, Laspeyres (1871:306) suggested the index formula that was later to carry his name. This suggestionelicited an immediate and pointed response from Drobisch (1871c: 423):

“However, also this formula is not new. As Laspeyres could have seenin my first paper, which he had available, I initially tried this approachmyself to calculate price increases and I described the reasons that per-suaded me not to continue with this approach.”

This crucial phrase verbalizes the undeniable facts concerning this unfortunatehistorical incident. In the end, the scientific recognition for the discovery of thetwo most widely known price indices today was erroneously bestowed. It brings tolight, however, Moritz Wilhelm Drobisch’s culpability in this scholarly dispute aswell. He rejected these price indices as inappropriate for price inflation measure-ments and instead formulated the unit value index, the index formula he consideredto be optimal. The tragedy of this episode lies in his failure to recognize the in-herent inconsistencies present in the unit value index due to the manner in whichhe formulated it. Everything considered, however, even though his foray into thefield of price statistics was a brief one, the lasting contributions he made are indeednoteworthy.The purpose of this paper is to convey information and, additionally, to produce

a greater awareness concerning this important scholar. It attempts to give creditwhere credit is due, but more importantly; it tries to put this unfortunate historicalincident into its proper perspective. Consequently, the paper proceeds as follows.Section 2 contains a short description of the pioneering contributions to price indextheory made by Moritz Wilhelm Drobisch. Economists and statisticians alike knowlittle about his personal and professional life and, therefore, a brief summary isprovided in Sections 3 through 5. Section 6 contains a eulogy and the concludingremarks are contained in Section 7.

2 Contribution

Wilhelm Georg Friedrich Roscher (1817-1894), ordentlicher Professor (Professor)at the Faculty of Philosophy of Universität Leipzig, was the person who arousedDrobisch’s interest in price index theory. Roscher was the founder of an approachto academic economics that is known the Ältere Historische Schule der Ökonomie(early Historical School of Political Economy). He was considering the problem:How should the mean price change of N different items between some base timeperiod, t = 0, and a comparison period, t = 1, be calculated, if it is assumed

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that the same N items are sold in the marketplace in both time periods? He wasundecided whether the price index formula proposed by Carli (1764),

PC =1

N

X p1ip0i

,

or the one proposed by Jevons (1863),

PJ =N

vuut NYi=1

(p1i /p0i ) ,

where pti is the price of item i (i = 1, . . . , N) observed in time period t andPis

used to denotePN

i=1, would yield the most suitable result.3 Therefore, he asked his

senior colleague Drobisch (1871a: 44; 1871c: 417, footnote 3) for some guidance.Drobisch was lecturing in the areas of mathematics and philosophy at the time

and his interest in the subject was stimulated by this request. He agreed to look intothe issue. In his treatise, Drobisch (1871a: 32-33) recognized that various items havedifferent purchase relevancies among consumers. Accordingly, a price index formulashould give stronger weights to the price developments of the highly relevant itemsand lesser weights to the others. Therefore, a proper price index formula must takeinto account the quantities transacted in the base, q0i , and comparison time periods,q1i . This led him to reject both the Carli and Jevons indices in search of a moreappropriate solution to the problem. He asked himself: How should the relevanceof an item be represented in a price index formula?In a preliminary step, Drobisch (1871a: 35) stated that all of the quantities

should be measured in a common unit of weight (Zentner = 50 kg.) and, con-sequently, the prices of the items involved would need to be adjusted accordingly.This could be accomplished by multiplying the original quantity data, qti , and divid-ing the original price data, pti, by some transformation factor, zi. Drobisch did notexplicitly use transformation factors but directly employed the converted quantities,q̃ti = qtizi, and prices, p̃

ti = pti/zi.

He approached the measurement problem from the standpoint of a simple scen-ario where the quantities transacted remained constant over time, q̃0i = q̃1i = q̃i. Forsuch a scenario, Drobisch (1871a: 36) proposed the following index formula:

PLo =

Pp̃1i q̃iPp̃0i q̃i

. (1)

Unbeknownst to him, however, Lowe (1822: Appendix 94-95) had proposed thisformula half a century earlier. Presently, it is known as the Lowe index, PLo.

3For an exposition of the early history of price index research see Balk (2008, Chapter 1) andDiewert (1993).

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He then progressed to a scenario with variable quantities, q̃0i 6= q̃1i . For thisscenario, Drobisch (1871a: 37-38) suggested two alternative formulas:

PL =

Pp̃1i q̃

0iP

p̃0i q̃0i

, (2)

and

PP =

Pp̃1i q̃

1iP

p̃0i q̃1i

. (3)

Subsequently, these two formulas have become known as the Laspeyres, PL, andPaasche, PP , indices. Drobisch stated that with unchanging quantities these twoformulas are equal to the previous formula, PLo. Furthermore, Drobisch (1871a:39) recognized that due to their inherent symmetry, both formulas are theoreticallyequivalent. He regarded this equivalence as a serious weakness. Drobisch (1871c:425) indicated, however, that the arithmetic mean of these indices could be used asa measure of price change:

PD =PL + PP

2.

Even though he considered this formula as unsatisfactory, some price statisticianspresently denote it as the Drobisch index, PD.His preferred price index, however, was a somewhat different one. In the deriv-

ation of this index, Drobisch (1871a: 39) took as the point of departure the unitvalue formula:

P tUV =

Pp̃tiq̃

tiP

q̃ti, for t = 0, 1 . (4)

In the previous year, Segnitz (1870: 184) had proposed the unit value formula(4) in an article published in this journal, a fact that Drobisch (1871a) failed tomention. Segnitz cautioned, however, that the use of this formula should be limitedto homogenous items and the example he gave was different quantities of the cerealgrain, rye. When heterogeneous items are considered the situation becomes muchmore complicated. These items are denominated in a variety of different unitsof measure and, as a result, the summation,

Pq̃ti , yields a meaningless number.

Drobisch was aware of this problem and thought he had the appropriate solution inhand. He believed that by measuring the quantities in a common unit of weight,the Zentner, and adjusting the prices accordingly, he had solved the problem.Consequently, Drobisch (1871a: 39) defined the unit value index, PUV , as the

ratio of two unit values:

PUV =P 1UVP 0UV

=

Pp̃1i q̃

1iP

p̃0i q̃0i

Pq̃0iPq̃1i

. (5)

Drobisch (1871a: 39; 1871c: 422-423) pointed out that with constant quantities,q̃0i = q̃1i = q̃i, this formula simplifies to his previous proposal (1) and also to hisother proposals (2) and (3).

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Drobisch regarded his unit value index (5) as superior to all other price indexformulas.4 He recognized that combining heterogeneous items into an aggregatequantity presents a problem but he was confident that his weight-related conversionscheme had solved it. Unfortunately, he failed to recognize that this weight-relatedconversion method involves a summation,

Pq̃ti , that could require combining some

very different items, for example, a Zentner of butter and a Zentner of indigodyestuff. Although these items have equal weight, they have extremely differentmonetary values. This invalidates the unit values calculated by formula (4) and,therefore, the unit value index (5) as well. Moreover, this weight-related conversionof prices and quantities is not even possible when intangibles such as services areinvolved.In their responses to Drobisch’s (1871a) proposals, Laspeyres (1871: 307) and

Paasche (1874: 172) both expressed their reservations regarding the unit value index(5). Laspeyres saw no problems involved with the proposal to transform all of thedata into a common weight based unit of measure. He criticized Drobisch, however,on the grounds that the unit value index formula allowed the quantities to changeover time. He suggested that the base period quantities, q̃0i , should prevail during thecomparison period as well, which yields index formula (2). This index today bearshis name. Furthermore, Laspeyres (1871: 308) pointed out that the unit value index(5) violates the Identity Axiom. This axiom postulates that with constant prices, aprice index should equal one regardless of the changes in the quantities that mighttake place.Paasche (1874: 172), on the other hand, suggested taking the comparison time

period quantities, q̃1i , as fixed. Consequently, he advocated formula (3). Today thisindex is known as the Paasche Index. Drobisch (1871a) first proposed it as well,although, he subsequently rejected it. Paasche (1874) did not mention Drobisch’scontribution at all, while Laspeyres (1871: 305) did recognize that the written re-commendations expounded by Drobisch (1871a: 30) would lead to the correct indexformula.From today’s perspective, the price statistical research of Moritz Wilhelm

Drobisch seems to contain a surprising lack of consistency. The astute research qual-ities he demonstrated in the derivation and analysis of the Laspeyres and Paascheindices stand in stark contrast to his failure to recognize the obvious inconsistenciesof his weight-related unit value index (5) when it is applied to heterogeneous items.Nevertheless, the legacy that he leaves behind in the field of official price meas-

urement cannot be overlooked. As a rule, statistical agencies compute price inflationestimates by comparing prices in a base time period to those in a comparison periodutilizing a two-stage process. The elementary level is concerned with the pricechanges of individual items. An item is a narrowly defined group of products that

4Lippe (2007: 18, footnote 43) points out that Drobisch’s unit value index should not beconfused with the unit value index used in some statistics of foreign trade.

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should be as homogeneous as possible. The official recommendation of ILO et al.(2004: 164) is to compute these price changes using Drobisch’s unit value indexformula (5). The upper level of price measurement is concerned with aggregatingthe unit values and quantities computed at the elementary level into an overall pricechange. This is most often accomplished utilizing a Laspeyres or Paasche type priceindex. Moritz Wilhelm Drobisch proposed both of these index formulas. There-fore, the complete process of official price measurement relies upon concepts that hedevised.His contribution, however, goes even further. Drobisch (1871a) considered his

unit value index (5) to be appropriate for the upper level of price aggregation as well.Some fourteen years later, Lehr (1885) studied his work and concluded that the unitvalue index formula (5) is a useful concept but the weight-related conversion relieson an incorrect basic premise. In order to illustrate Lehr’s consideration, formula(5) can be expressed in an alternative form. Utilizing the transformation factors, zi,the original quantities, qti , and the original prices, p

ti, formula (5) can be expressed

in the following manner:

PUV =

Pp1i q

1iP

p0i q0i

Pq0i ziPq1i zi

. (6)

Lehr (1885: 38-39) recognized that in order to make the summation,P

qtizi, mean-ingful, the units in which the quantities, qtizi ,are measured had to be of comparablevalue and not simply of comparable weight. Therefore, he proposed the followingscheme for the calculation of the transformation factors:

zi =p0i q

0i + p1i q

1i

q0i + q1i, for i = 1, 2, ..., N . (7)

Substituting this result into formula (6) yields the Lehr index. A number of yearslater, Davies (1924: 185) made a similar proposal. Instead of formula (7), he pro-posed the following formulation for the transformation factors:

zi =qp0ip

1i , for i = 1, 2, ..., N .

Substituting this result into formula (6) yields the Davies index. Auer (2009) demon-strated with a systematic analytical elaboration that the proposal of Davies (1924:185) is a member of a specific set of price indices. Auer named this set the gener-alized unit value indices and demonstrated that the Laspeyres and Paasche indicesare also members of this particular family.Drobisch’s (1871a,b,c) short excursion into price index theory resulted in a con-

siderable boon for this area of research. He developed the unit value index (5), aswell as the Laspeyres (2) and Paasche (3) indices. Who was this distinguished Ger-man scholar? Why is it that he is not better known among researchers within thefield? Fortunately for us, eight years after his passing one of his grandsons, WaltherNeubert-Drobisch (1902), wrote an illuminating biography based upon a collection

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of diaries and letters that he had inherited. Much of the information hereinafterrelies upon this informative source.

3 Adolescence

Moritz Wilhelm Drobisch’s father, Karl Wilhelm Drobisch, was a religious and patri-otic man.5 Raised in a rather poor family, due to his diligence and persistent nature,he, nevertheless, attained the respected position of Stadtschreiber (city clerk) in thecity of Leipzig. At that time, Leipzig was an important and wealthy city in theKingdom of Saxony. He was content in his marriage, even though he and his wifesuffered the loss of four of their six children. Only two of their daughters lived bey-ond childhood. In 1790, at the age of thirty-five, his beloved wife passed away. Herecuperated from this loss, however, and was able to remarry four years later. Hemarried Renata Dorothee Wilhelmine Klotz, the thirty-three year old daughter of astate judicial employee from Grimma, a small town located southeast of Leipzig onthe Mulde River.After seven years of a childless marriage, on the sixteenth of August 1802 the

couple was blessed with their first child, Moritz Wilhelm Drobisch. On ChristmasEve the following year, Karl Ludwig was born. Karl Ludwig was later to become awell known music teacher, conductor, and composer. At a young age, the two boyslost their twenty-eight year old stepsister in 1809. This was a tragic loss and onethat their father never fully recovered from.Nevertheless, as the boys grew older, their father taught themmany things. Con-

sequently, they could already read, write, and were performing some basic mathem-atical calculations long before they entered primary schooling at the Nicolaischule(Nikolai School) in Leipzig. Education played an important role in the Drobischhousehold and, as a result, the boys came to view their father’s study as if it weresome kind of “holy” room. Their minds were quite engaged during these formativechildhood years as they eagerly embraced many new ideas. For example, MoritzWilhelm and his younger brother enjoyed stargazing late into the night from theroof of their home. The two boys became very interested in astronomy and begancalculating the phases of the moon, the movement of the planets, and soon they hadlearned the names of the most famous constellations.From October the 16th to the 19th, 1813, the Völkerschlacht bei Leipzig (Battle

of the Nations) took place on the outskirts of the city. Moritz Wilhelm was el-even years old at the time and watched the ensuing battle from the roof with histelescope. At its conclusion, he was fortunate enough, from a short distance, towitness King Friedrich I of Saxony offer the defeated Napoleon Bonaparte a glass

5Apart from where otherwise noted, this section is based upon the biography by Neubert-Drobisch (1902: 1-20).

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of wine. Napoleon hastily drank the wine and, in a mood of desperation, angrilythrew the empty glass to the ground. What he had just seen made a strong andlasting impression upon young Moritz Wilhelm’s mind. To him it symbolized howthe unrealized ambitions of Napoleon and those of his ally the Kingdom of Saxonywere now laid at their feet like the glistening shards of the shattered wine glass. Hedecided then and there to fully develop his physical and mental skills and to becomea strong contributor for his fatherland.Regrettably, however, this idyllic childhood, one that played such an important

role in the boys’ early intellectual development, came to an abrupt end in 1815 withthe passing of their father. As a result, Moritz Wilhelm’s mother sent him awayto the prestigious Fürstenschule St. Augustin zu Grimma (secondary school) andKarl Ludwig followed two years thereafter. The money their father had bequeathedwas intended for this schooling and also for their subsequent university education.Moritz Wilhelm enjoyed his three years at the Fürstenschule and the fertile academicenvironment that existed there nurtured his preexisting interests in mathematicsand astronomy. This was in part due to his interactions with a gifted teacher whoengaged the young man in inspiring debates. To some extent, this teacher playedthe roll of a surrogate father for Moritz Wilhelm. In his free time, he continued toengross himself in his most important hobby, astronomy. As evening approached,he would eagerly look forward to secretly observing the stars with the equipment hepurchased with the pocket money he had saved. During these adolescent years hereturned to Leipzig infrequently, only to visit his mother during school vacations inthe summer months.On March 28th, 1820, at the age of seventeen, Moritz Wilhelm began studying

mathematics and physics at the Universität Leipzig. While most of his peers wereindulging themselves in the newly discovered freedom called “student life”, MoritzWilhelm gave his academic responsibilities first priority. It was said that more oftenthan not, he refrained from drinking beer and instead drank a glass of milk. Asa result, after just one year he was already giving private lessons in mathematics.With the money he earned he increased his personal library and added to his accu-mulation of astronomical instruments. He politely declined the private invitationsthat were offered by his professors for he feared that such engagements would in-hibit his personal and intellectual independence. During these initial years at theuniversity, he was an extremely purposeful and resolute young man.At the age of twenty, Moritz Wilhelm lost his dear mother on March 6th, 1822.

Consequently, he and his brother departed the family home in search of a newplace to live. They found a suitable room and rented it from the widow AnnaMaria Leichsenring. Two month later in May, Moritz Wilhlem, his brother, andanother fellow student hiked to the scenic Sächsische Schweiz via Grimma, Meißen,and Dresden. At the conclusion of this enjoyable trip, he returned to Leipzig a bitperplexed. He had decided, in the meanwhile, to turn his focus towards more cultural

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and worldly things and not any longer to devote himself solely to his scholarlyactivities. He became increasingly captivated by the arts. His appreciation for musicand literature, especially the works of William Shakespeare, grew. It was during thisperiod of uncertainty that Moritz Wilhelm became acquainted with Emilie CharlotteLeichsenring, one of his landlady’s three daughters. He had begun to write poetryand during this courtship, which ultimately lasted five years, he wooed her withmany of his delightful poems. He enjoyed writing poetic prose and did so for theremainder of his life. This interlude into belletristic literature, however, was briefand lasted only a year and a half. He stated at its conclusion, “The reading of novelshad corrupted me.” After some soul searching, he recommitted himself to the studyof mathematics and the sciences. The appreciation for music and the arts that hehad gained, however, never left him.

4 Adulthood

Moritz Wilhelm Drobisch returned to being an exceedingly focused and studiousyoung man.6 He completed his studies at the Universität Leipzig in the Faculty ofPhilosophy in four years. In 1824, at the young age of twenty-two, he received theacademic degree of Dr. phil. in Mathematik (Ph.D.-Mathematics) with a disserta-tion entitled: Praemissae ad theoriam organismi generalem, theoriae analyseos geo-metricae prolusio (An Introduction to the Theory of Analytical Geometry). Duringthat same year he was granted his Habilitation in Philosophy (postdoctoral lecturequalification) and became a Privatdozent (qualified external lecturer). It had alwaysbeen his ambition to become a teacher at a höhere Schule (secondary school) and sohe felt very fortunate to be able to teach at the university level. Before long he wasgiving lectures in several mathematical subjects, physical geography, and popularastronomy. In 1826, at the age of twenty-four, he was appointed außerordentlicherProfessor (Adjunct Professor) in the Faculty of Philosophy and by the end of thatsame year, following a proposal of the government and not the university, he wasselected to be ordentlicher Professor (Professor) of Mathematics. Unfortunately,the appointment was not without its controversy because some of the older facultymembers voiced strong opposition to the appointment. They believed that he wastoo young and lacked the required experience for the position. One of his support-ers, however, came to his rescue by sarcastically suggesting that Dr. Drobisch’s“mistakes” would surely diminish with the passage of time.The meteoric ascent of his academic career, culminating in the attainment of a

professorship, offered him the prospect of entering into a prearranged marriage ofconvenience with one of the most influential families in Leipzig. Like his father beforehim, however, he resisted the temptation. He had no great craving for one of those

6Apart from where otherwise noted, this section is based upon Neubert-Drobisch (1902: 21-49).

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frivolous, overly satiated rich daughters, instead he desired a woman who would bea proper mother for his yet to be born children and a skillful homemaker. In 1827,on the thirteenth day of September he married Emilie Charlotte Leichsenring. Amarriage that was to last some forty-four years and one that was to be blessed withfive daughters and three sons. Their initial happiness, however, was not destined last.As parents, they were forced to endure the tragic loss of five of their beloved children.Only three of their daughters survived. Consequently, as he grew older he becameincreasingly spiritual and devout in his beliefs. He cautioned that scientists shouldnot be condescending towards religious faith and that they should not attempt toplace themselves above it.7

He delivered his first lecture on philosophy in 1832. This event proved to be amilestone in his professional career for it marked the start of a long process wherehe shifted his intellectual emphasis away from mathematics towards philosophy.Ten years later in 1842, he was appointed ordentlicher Professor (Professor) ofPhilosophy.8 He resigned his professorship in mathematics in 1868, a position heheld for forty years. From that point on he devoted his scholarly activities to thefields of philosophy and psychology.9

The person who had the greatest scientific influence upon him was the philo-sopher, psychologist, and pedagogue, Johann Friedrich Herbart (1776-1841), Pro-fessor of Philosophy at Universität Göttingen. Prof. Herbart recognized his uniquecapacity to integrate philosophy and mathematics and appreciated it as an outstand-ing scientific trait. To commemorate his death in 1841, Prof. Drobisch delivered apoignant eulogy in his honor. Shortly afterwards he was approached by a group ofstudents who asked his permission to commission a portrait of his likeness. Pleasedby the gesture, he agreed and prepared a comment for inscribing at the base of thelithograph (see Figure 2).

“The flame of bona fide scienceis kindled by the spark of inspiration,

it nourishes itself from the fuel of hard work andburns undimmed only in the breath of freedom.”

(„Die Flamme der echten Wissenschaft

entzündet sich an dem Funken der Begeisterung,

nährt sich von dem Öl des Fleißes und

brennt ungetrübt nur in der Lebensluft der Freiheit.“)

Moritz Wilhelm Drobisch seldom left his much-loved city of Leipzig. He feltcompletely at home there and was intimately linked to its university. Occasionally,

7Neubert-Drobisch (1902: 64).8Neubert-Drobisch (1902: 79).9Neubert-Drobisch (1902: 123).

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Figure 2: Prof. Drobisch, 1841; Source Neubert-Drobisch (1902: inner cover).

however, he was called upon to travel. In these instances he complied dutifully anddid so either in the company of his wife or alone.10 He was a reluctant traveler, unlessof course, the trip was one of his periodic “escapes” into the scenic countryside thatsurrounded Grimma. There he could find the solace and happiness he sought ashe nostalgically immersed himself in the memories of his adolescent school days atthe Fürstenschule. Afterwards, when he returned to his everyday responsibilities inLeipzig, he always felt a sense of renewal and invigoration.11

The death of his beloved wife Emilie Charlotte in 1871 was a hard blow.12 Indifficult moments, however, he quietly spoke words of encouragement to himself andfound solace in his work. Many years before, he had written the following poeticlines:13

10Neubert-Drobisch (1902: 58ff., 67ff., 109ff., 119).11Neubert-Drobisch (1902: 35f., 54).12Neubert-Drobisch (1902: 125).13Neubert-Drobisch (1902: 49).

13

“Never mind the transition from day to night,Heed not the cyclic change of the seasons,Engross yourself in the depth of knowledge,

Produce things of significance, worth, and veracity;Then you will be contented for the moment,And the days will tacitly run their course.”

(„Vergiß den Wechsel von Tag und Nacht,

Vergiß die Wechsel des Jahres,

Vertiefe Dich in des Wissens Schacht,

Schaff Hohes, Edles und Wahres;

Dann bist Du glücklich im Augenblick,

Und still trägt jeder Tag sein Geschick.“)

5 Academic

Moritz Wilhelm Drobisch placed great emphasis on his teaching assignments.14 Anextremely hard working and conscientious professor, he took great pride in meticu-lously preparing his lectures.15 In addition to his customary lectures in mathematicsand philosophy, he also conducted lectures in such diverse fields as psychology, popu-lar astronomy, physical geography, logic, and the philosophy of religion. His lectureswere clearly presented, well organized, and scientifically precise. The solutions to theproblems he posed were presented in a logical and lucid manner. His lively lecturingstyle was highly valued by the students at the Universität Leipzig and his personalvitality allowed him to continue teaching well into his octogenarian years. Finally,at the age of eighty-four, he requested to be released from his responsibilities as alecturer due to an eye complaint.16

His style of writing, as evidenced by the books and numerous scientific articleshe published, was characterized by a high degree of finesse, clarity, and precision.17

Initially, his scholarly work dealt solely with mathematically related subjects. As heaged, however, his primary interest began to shift ever more towards the philosoph-ical and psychological bodies of thought. Subsequently, these were the areas wherehe received considerable acclaim. Nevertheless, during the later part of the 1860’she began to have an increased interest in statistical topics. Regrettably, however,his two articles in 1871 were his only foray into the field of price statistics.In spite of his teaching and extensive research activities, over the years he served

in numerous administrative capacities for the university. He did not solicit theseadditional academic responsibilities because he viewed them as a hindrance to his

14Apart from where otherwise noted, this section is based upon Neubert-Drobisch (1902: 73-128).15Heinze (1896: 713ff.).16Heinze (1896: 699).17Heinze (1896: 699f.).

14

primary duties. Nevertheless, he served as Dekan (Dean) of the Faculty of Philo-sophy on eight separate occasions and as a member of the faculty senate. He wasthe Rektor der Universität Leipzig (president) during 1841 and 1842. As Rektor heofficially represented the university at numerous governmental meetings, scientificcongresses, and at formal social gatherings. He did so dutifully but would have muchpreferred the solitude of his hiking tours in Saxony’s scenic countryside.18 He re-marked later, however, that the experiences he had as Rektor helped save him frombecoming a complete scientific recluse and forced him to live the life of a man of theworld. During the meager amount of free time that he allowed himself, however, heespecially enjoyed attending concerts at the Gewandhaus zu Leipzig (Concert Hall)where Felix Mendelssohn Bartholdy (1809-1847) was the Gewandhauskapellmeister(conductor) from 1835 to 1847.

Figure 3: Prof. M. W. Drobisch, cir. 1877; Source: Wiemers (2003).

In addition to all this, he was a Mitglied (member since 1834) as well as laterPräsident (Chairman, 1848-1863) and Ehrenmitglied (honorary member, 1877) ofthe Fürstlich Jablonowskische Gesellschaft der Wissenschaften zu Leipzig (PrinceJablonowski Scientific Society of Leipzig), an organization that encouraged scientificwork through the awarding of prizes. Laspeyres (1862) won such a prize for his studyof the economics’ literature and the history of economic thought in the Netherlandsduring the period 1600 to 1785. As Chairman of the society, he advocated its mod-ernization and wanted to transform it into a scientific society that published originalresearch. He failed in this attempt, however, because he could not change the con-stitution of the organization. As a result, he founded the independent Königliche

18Neubert-Drobisch (1902: 54).

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Sächsische Gesellschaft der Wissenschaften (Royal Scientific Society of Saxony) andon July 1st, 1846, he delivered the inaugural address on the occasion of the 200thanniversary of the birth of Gottfried Wilhelm Leibniz. He wrote the constitutionhimself and firmly established the independence of the new society from the Uni-versität Leipzig. He made it clear that the main objective of the society was thepublication of research and one such publication was Drobisch’s (1871a) own treatiseon price statistics.19

To commemorate the fiftieth anniversary of his professorship in 1876, MoritzWilhelm Drobisch was ceremonially proclaimed Ehrenbürger der Stadt Leipzig (hon-orary citizen) at the Rathaus (City Hall). He received the title of the highest officialof the royal court, Königlich Sächsischer Hofrat, 1862, and Geheimer Hofrat, 1866,(Court Counselor). He was decorated with numerous medals including, Ritterkreuzdes Königlich Sächsischen Civil-Verdienstordens, 1844, and the Comthurkreuz dessächsischen Albrechtordens, 1877. He accepted all of these honors gratefully and withhumility, but was of the opinion that he had earned none of them. The KöniglicheSächsische Gesellschaft der Wissenschaften recognized Prof. Drobisch for his roleas their founding father with the creation of the Moritz-Wilhelm-Drobisch-Medaillein 1971.20

6 Eulogy

Moritz Wilhelm Drobisch was considered to be a very honorable and trustworthyperson.21 It was said that he personified the “kategorische Imperativ” (CategoricalImperative) formulated by Immanuel Kant (1724 — 1804), the great 18th centuryGerman philosopher. This fundamental ethical principle guided his actions as hedetermined what was morally right throughout the course of his life. A devoutChristian who followed the Protestant faith, he lived by a set of moral guidelinesthat led him to be a respectful, honest, and unassuming man. Consequently, onthe occasion of the fiftieth anniversary of his professorship, these virtuous charactertraits were revealed when he donated all of the monetary gifts he received to benefitfinancially disadvantaged students.22

In his dealings with strangers, he was always very considerate and extremelypolite. Nevertheless, on these occasions he would often appear quite serious. Thiswas sometimes misconstrued and it was said that he distrusted those he did notknow well. This was not the case. At social functions such as birthday parties,confirmations, weddings, or other such festive occasions, he would display a quite

19Wiemers (2003: 9ff.).20Wiemers (2003: 16).21Apart from where otherwise noted, this section is based upon Neubert-Drobisch (1902: 127-

131).22Heinze (1896: 718).

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amiable demeanor. He would amuse others with his cordial, albeit slightly sarcasticpersonality. Sometimes he would even entertain guests with his own poetry, poemsof both a serious and a humorous nature.23

Towards the end of his long and fruitful life, Moritz Wilhelm Drobisch remainedintellectually active and spry. He became, however, more and more reclusive. Hav-ing outlived his dearly beloved wife Emilie Charlotte by a quarter of a century aswell as a substantial number of his closest university colleagues, while experiencingacutely the associated loneliness, he displayed his characteristic humility and devoutspirituality by leaving behind this moving testimonial:24

“I have lived long and strived relentlessly,Attempted much, alas I achieved little.More than my worth, I was venerated,

Unmerited fortune was bestowed upon me.Only this attestation may I make,

That I endeavored to live a dutiful life.Whenever I strayed from the path of righteousness,

I humbly trust in the grace of GodAnd into the loving hands of the LordI entrust my final days and my demise.”

(„Lange hab’ ich gelebt und gestrebt,

Viel gesponnen, doch wenig gewebt.

Mehr als ich wert war, ward ich geehrt,

Mehr als Verdienteren Glück mir beschert.

Nur das Zeugnis darf ich mir geben,

Daß ich bemüht war, pflichttreu zu leben.

Wo ich gewichen vom rechten Pfade,

Hoff ’ ich in Demut auf Gottes Gnade

Und in des liebenden Vaters Hände

Leg’ ich den Lebensrest und mein Ende.“)

Moritz Wilhelm Drobisch died in Leipzig shortly before the seventieth an-niversary of his professorship on September 30th, 1896. He was ninety-four yearsold.

7 Conclusion

Moritz Wilhelm Drobisch was a multifaceted scholar who held the academic posi-tions of Professor of Mathematics and Professor of Philosophy, both separately and23Neubert-Drobisch (1902: 49).24Neubert-Drobisch (1902: 131).

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Figure 4: Moritz Wilhelm Drobisch in His Study at the Age of 90; Source: Neubert-Drobisch (1902: 96b).

concurrently, at the Universität Leipzig over a tenure lasting some sixty-eight years.His scientific contributions were insightful and varied, for he was equally at home ina wide variety of scholarly disciplines.In 1871, his scientific curiosity led him into the field of price statistics. It remains

to this day an unresolved mystery, however, regarding the question: Why was hisinterest in price statistics so brief, lasting only one year? One can only speculate.Was it his scholarly dispute with Étienne Laspeyres? Certainly that robbed him ofmuch of the satisfaction associated with his scientific contributions in this area. Hehad reached the age of sixty-nine and the bereavement associated with the death ofhis beloved wife during that same year certainly added a great emotional burden.The professorship he held in mathematics for forty-two years had previously beenresigned three years earlier. As a result, his scholarly interests were shifting awayfrom mathematically related subjects towards those of a philosophical and psycho-logical nature. He entered the field of price statistics at the request of a facultycolleague and after formulating the unit value index he probably felt that he hadfound the optimal answer to the question. Perhaps he felt that his work in thisarea was complete. All of these factors probably played a role. If his contributionshad been received in a more positive way, then would he have lingered for a longerperiod in the area of price statistical research? This intriguing mystery will remain

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unsolved.The scientific recognition for the discovery of the two most widely known price

indices today was erroneously bestowed. Moritz Wilhelm Drobisch’s culpability inthe course of events that lead to this outcome, however, must not be overlooked.At the time, he rejected these two price indices as inappropriate for price inflationmeasurements and instead formulated the unit value index. The tragedy of thisepisode, however, lies in his failure to recognize the inherent inconsistencies presentin his favored index due to his fixation upon a weight-related formulation.It is certain, however, that Moritz Wilhelm Drobisch’s brief but fruitful foray

into the field of price statistics yielded a quantum leap in this branch of science.He enriched the field with the introduction of three fundamental index concepts:the Laspeyres, the Paasche, and the unit value index. With these three indices helaid the theoretical cornerstone upon which price index methodology has been built.These formulas are the key for the official inflation measurements that are madearound the world today. The seminal contributions he made were significant andshould be appropriately acclaimed and acknowledged.

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Wiemers, G. (2003), Moritz Wilhelm Drobisch und die Gründung der KöniglichSächsischen Gesellschaft der Wissenschaften zu Leipzig, 1846. Abhandlun-gen der Sächsischen Akademie der Wissenschaften zu Leipzig, Mathematisch-naturwissenschaftliche Klasse, Vol. 60(3): 7-16.

Author:Ludwig von AuerUniversität TrierFachbereich IV — FinanzwissenschaftUniversitätsring 15D-54286 Trier, Germany

tel.: +49 (651) 201 2716fax: +49 (651) 201 3968Email: vonauer@uni-trier.de

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